Question

prove that (A-B)-C=A-(B U C)
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Answer 1

Answer:

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Answer 2

PROOF OF (A−B)−C=A−(B∪C)  

Step-by-step explanation:    

Proof: Let x ∈(A−B)−C    

• ⟹x∈(A−B)∧x∉C    

• ⟹x∈A∧x∉B∧x∉C    
• ⟹x∈A∧x∉B∪C    
• ⟹x∈A−(B∪C)    
• ⟹(A−B)−C⊆A−(B∪C)----------(1)  
• Let x ∈A−(B∪C)    
• ⟹x∈A∧x∉B∪C    
• ⟹x∈A∧x∉B∧x∉C    

• ⟹x∈A−B∧x∉C    
• ⟹x∈(A−B)−C    
• ⟹A−(B∪C)⊆(A−B)−C-------(2)  
• by equating (1) and (2), we get  

• (A−B)−C=A−(B∪C).